When the alarm "starts" , what is it doing? More horn beeping?
Your issue reminds me of the SECURITY problem on the next earlier generation of Impalas. There is a sensor in the ignition cylinder that detects the presence of the key. The connection to the BCM was known to be iffy resulting in the BCM not allowing the car to be started because it could not detect the key in the cylinder.
In your case, you remove the key, and you get 3 beeps. Make sure you are turning the cylinder all the way to off. On cars with some age, the cylinders will sometimes allow the key to be pulled out without the cylinder turned fully counter-clockwise. So that would leave the ignition switch not fully off, but no key in the cylinder. I'm wondering if that could cause a security issue on this model.
The car always starts, right? The only issues are the 3 beeps and the alarm, but the car otherwise starts and runs?
Doug
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